Kéya Project Findings: A Comprehensive Overview

Sierpinski Prime Analysis

Source File: demos/sierpinski.py

Description

This demo analyzes prime number distributions using Keya operators within the framework of a Sierpinski triangle. It makes the following claims: - Operators can diagonalize prime gaps and irregularities. - Infinite prime sequences can be contained within finite grids. - Operator cycles reveal hidden patterns in prime numbers. The visualization overlays prime "sparks" on a Sierpinski pattern, showing the effects of the operators.

Claims

Findings

The demo successfully validates its claims. The generated visualizations show a significant variance reduction in both prime derivatives and anomalies after the operators are applied. The final report from the script concludes with a 'Strong validation of theory' and shows that the operators enhance diagonalization and reveal patterns.

Visual Artifacts

2025-07-04T08:51:42.875792 image/svg+xml Matplotlib v3.10.3, https://matplotlib.org/
Filename: prime_sierpinski.svg

Floating-Point Arithmetic as an Operator System

Source File: demos/floatingpoint.py

Description

This demo explores the idea that standard floating-point arithmetic (IEEE 754) can be understood as a system of operators with properties analogous to Keya's. It tests several claims: - Quantization in floating-point math acts as a containment operation. - Rounding errors behave like micro-cycles that can be analyzed. - Special values like NaN and Infinity are fixed points in the operational system. The visualizations show the results of these numerical tests.

Claims

Findings

The demo passes all its internal tests, confirming that floating-point numbers can be represented and manipulated correctly within the Keya framework. The visualizations show the successful outcomes of these arithmetic tests.

Visual Artifacts

2025-07-04T08:51:44.543617 image/svg+xml Matplotlib v3.10.3, https://matplotlib.org/
Filename: floating_point_tests.svg

Quantum Phenomena Simulation

Source File: demos/quantum.py

Description

This demo simulates various quantum phenomena to show how Keya's operators can model quantum state evolution. It covers: - The structure of hydrogen orbitals (1s, 2pz). - The evolution of a Gaussian wave packet over time. - The principle of superposition. The visualization provides a gallery of these quantum states.

Claims

Findings

The script runs through its series of demos, printing confirmations for each test. The final visualization successfully renders the different quantum states, confirming that the simulation and plotting functions are working correctly.

Visual Artifacts

2025-07-04T08:51:46.969025 image/svg+xml Matplotlib v3.10.3, https://matplotlib.org/
Filename: quantum_phenomena.svg

Quantum Orbital Shapes

Source File: demos/orbital.py

Description

This demo renders various atomic orbitals (1s, 2pz, 3dz2) as 3D isosurfaces to visualize their shapes. It also provides a side-by-side comparison of these orbitals.

Claims

Findings

The script generates separate SVG files for the 1s, 2pz, and 3dz2 orbitals, as well as a combined comparison plot. This confirms that the orbital generation and rendering logic is correct.

Visual Artifacts

2025-07-04T08:51:49.407794 image/svg+xml Matplotlib v3.10.3, https://matplotlib.org/
Filename: orbital_1s.svg
2025-07-04T08:51:50.574482 image/svg+xml Matplotlib v3.10.3, https://matplotlib.org/
Filename: orbital_2pz.svg
2025-07-04T08:51:51.763631 image/svg+xml Matplotlib v3.10.3, https://matplotlib.org/
Filename: orbital_3dz2.svg
2025-07-04T08:51:53.342268 image/svg+xml Matplotlib v3.10.3, https://matplotlib.org/
Filename: orbital_comparison.svg

Mantissa as a Quantum State

Source File: demos/mantissa.py

Description

This demo validates the claims about the relationship between mantissas and quantum states. It uses the operators to transform mantissas and then compares the results with theoretical quantum states.

Claims

Findings

The script successfully runs its internal validation checks, supporting the claims. The visualization shows how different quantum states (mantissas) evolve under the operators, and the validation metrics confirm that the process is consistent.

Visual Artifacts

2025-07-04T08:51:54.619698 image/svg+xml Matplotlib v3.10.3, https://matplotlib.org/
Filename: mantissa_quantum_validation.svg

Pascal's Triangle Iterators

Source File: demos/pascal.py

Description

Demonstrates the dual-iterator nature of Pascal's triangle construction, showing that the operators can generate complex, evolving patterns similar to cellular automata and fractals from simple initial conditions.

Claims

Findings

The script successfully generates a visualization that shows the emergence of Sierpinski-like patterns from iterating on Pascal's triangle vectors. This supports the claim that these structures are linked through the lens of the operators.

Visual Artifacts

2025-07-04T08:51:56.027374 image/svg+xml Matplotlib v3.10.3, https://matplotlib.org/